2(x^2-40)=-x^2+6(x-4)+1

Solution for 2(x^2-40)=-x^2+6(x-4)+1 equation:

Simplifying
2(x2 + -40) = -1x2 + 6(x + -4) + 1

Reorder the terms:
2(-40 + x2) = -1x2 + 6(x + -4) + 1
(-40 * 2 + x2 * 2) = -1x2 + 6(x + -4) + 1
(-80 + 2x2) = -1x2 + 6(x + -4) + 1

Reorder the terms:
-80 + 2x2 = -1x2 + 6(-4 + x) + 1
-80 + 2x2 = -1x2 + (-4 * 6 + x * 6) + 1
-80 + 2x2 = -1x2 + (-24 + 6x) + 1

Reorder the terms:
-80 + 2x2 = -24 + 1 + 6x + -1x2

Combine like terms: -24 + 1 = -23
-80 + 2x2 = -23 + 6x + -1x2

Solving
-80 + 2x2 = -23 + 6x + -1x2

Solving for variable 'x'.

Reorder the terms:
-80 + 23 + -6x + 2x2 + x2 = -23 + 6x + -1x2 + 23 + -6x + x2

Combine like terms: -80 + 23 = -57
-57 + -6x + 2x2 + x2 = -23 + 6x + -1x2 + 23 + -6x + x2

Combine like terms: 2x2 + x2 = 3x2
-57 + -6x + 3x2 = -23 + 6x + -1x2 + 23 + -6x + x2

Reorder the terms:
-57 + -6x + 3x2 = -23 + 23 + 6x + -6x + -1x2 + x2

Combine like terms: -23 + 23 = 0
-57 + -6x + 3x2 = 0 + 6x + -6x + -1x2 + x2
-57 + -6x + 3x2 = 6x + -6x + -1x2 + x2

Combine like terms: 6x + -6x = 0
-57 + -6x + 3x2 = 0 + -1x2 + x2
-57 + -6x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-57 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-19 + -2x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-19 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-19 + -2x + x2 = 0

Solving
-19 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -2x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + -2x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2x + x2 = 0 + 19
-2x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
-2x + x2 = 19

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 19 + 1

Reorder the terms:
1 + -2x + x2 = 19 + 1

Combine like terms: 19 + 1 = 20
1 + -2x + x2 = 20

Factor a perfect square on the left side:
(x + -1)(x + -1) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + -1) equal to 4.472135955 and -4.472135955.

Subproblem 1
x + -1 = 4.472135955

Simplifying
x + -1 = 4.472135955

Reorder the terms:
-1 + x = 4.472135955

Solving
-1 + x = 4.472135955

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = 4.472135955 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.472135955 + 1
x = 4.472135955 + 1

Combine like terms: 4.472135955 + 1 = 5.472135955
x = 5.472135955

Simplifying
x = 5.472135955

Subproblem 2
x + -1 = -4.472135955

Simplifying
x + -1 = -4.472135955

Reorder the terms:
-1 + x = -4.472135955

Solving
-1 + x = -4.472135955

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = -4.472135955 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.472135955 + 1
x = -4.472135955 + 1

Combine like terms: -4.472135955 + 1 = -3.472135955
x = -3.472135955

Simplifying
x = -3.472135955

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.472135955, -3.472135955}
Solution
x = {5.472135955, -3.472135955}